Observables and Uncertainty Relations

Hui-Hui Qin, Shao-Ming Fei, Xianqing Li-Jost

We investigate the product form uncertainty relations of variances for n (n ≥ 3) quantum observables. In particular, tight uncertainty relations satisfied by three observables has been derived, which is shown to be better than the ones derived from the strengthened Heisenberg and the generalized Schrödinger uncertainty relations, and some existing uncertainty relation for three spin-half operators. Uncertainty relation of arbitrary number of observables is also derived. As an example, the uncertainty relation satisfied by the eight Gell-Mann matrices is presented.

Scott Corry

Qiu-Cheng Song, Jun-Li Li, Guang-Xiong Peng +1 more

Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty relation. Here we present a variance-based sum uncertainty relation for N incompatible observables stronger than the simple generalization of an existing uncertainty relation for two observables. Further comparisons of our uncertainty relation with other related ones for spin- and spin-1 particles indicate that the obtained uncertainty relation gives a better lower bound.

Minyi Huang

Uncertainty is a fundamental and important concept in quantum mechanics. In this work, using the technique in matrix theory, we propose an uncertainty relation of four observables and show that the uncertainty constant is tight. It is argued that this method can deal with the several known uncertainty relations for two, three and four observables in a unified way. The result is also compared with other uncertainty relations of four observables.